## Force On A Current

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# Force on a Current-Carrying Conductor in a Magnetic Field

Consider a straight conductor of length l and cross-sectional area A, carrying current i. It is placed in a field of magnetic induction B at right angles to the length of the conductor and directed into the plane of the paper.

The electric current, I, in a conductor is due to free electrons moving in a direction opposite to the direction of the electric current. Let n be the number of free electrons per unit volume of the conductor and vd the drift velocity of the electrons.

The magnitude of the force on each electron is

f = evd B. (. : vd _|_ B)

The number of electrons in the length l of the conductor is

N = n l A.

Therefore, total force on all the free electrons, i.e., on the length l of the conductor is

F = fN = (e vd B) N = (e vd B) (nlA) = (n Ae vd ) (Bl).

But n A e vd = i, the current n the wire

. : F = I Bl.

If the conductor makes an angle θ with the magnetic field induction B, then the force is

F = iBl sin θ.

or Vectorially, F = il x B.

Here, I is a vetor pointing along the straight conductor in the direction of the current.

Direction of F is perpendicular to both, I and B and is given by Fleming’s left hand rule.

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